Base Plate Verification Example
10
60 / DESIGN GUIDE 1, 2ND EDITION / BASE PLATE AND ANCHOR ROD DESIGN 2. Assume a 14-in. × 14-in. base plate. The effective ec- centricity is Then, e > e kern ; therefore, anchor rods are required to resist the tensile force. The anchor rods are assumed to be 1.5 from the plate edge. 3. Determine the length of bearing. thus, Determine required plate thickness: B.5.2 Example: Large Moment Base Plate Design, Triangular Pressure Distribution Approach Design the base plate shown in Figure B.4 for an ASD and LRFD required strength of 60 and 90 kips, respectively, and moments from the dead and live loads equal to 480 and 720 kip-in., respectively. The ratio of the concrete to base plate area (A 2 /A 1 ) is 4.0. Bending is about the strong axis for the wide flange column W8×31 with d = b f = 8 in.; F y of the base plate and anchor rods is 36 ksi and f c ′ of the concrete is 3 ksi. 1. LRFD ASD P M P A u u p = = = ≤ 90 720 0 60 0 85 3 0 2 0 60 1 7 1 kips kip-in. φ . (. )( . )( ) . (.)(.) 30 P M P A a a p = = = ≤ 60 480 085 30 2 2 50 17 30 1 kips kip-in. Ω (. )( . )( ) . ( . )( . ) . . 2 50 2 04 1 P A p Ω = ksi LRFD ASD e = 720 kip-in./90 kips = 8.00 in. e = 480 kip-in./60 kips = 8.00 in. Figure B.4. Design example with large eccentricity. LRFD ASD ′= × × = f 3 06 14 12 5 2 268 . . ksi in. kips ′= × × = f 2 04 14 12 5 2 178 . . ksi in. kips LRFD ASD A = − − × × × ( ) + × 268 268 4 3 06 14 6 90 55 720 3 06 14 3 2 . . . = in. 5 27 . A = − − × × × ( ) + × 178 178 4 2 04 14 6 60 55 480 2 04 14 3 2 . . . = in. 5 27 . φP A p 1 3 06 = . ksi AISC Design Guide 1, 2nd Edition Base Plate and Anchor Rod Design Verification Example
Transcript of Base Plate Verification Example
60 / DESIGN GUIDE 1, 2ND EDITION / BASE PLATE AND ANCHOR ROD DESIGN
2. Assume a 14-in. × 14-in. base plate. The effective ec-centricity is
Then, e > ekern; therefore, anchor rods are required to resist the tensile force. The anchor rods are assumed to be 1.5 from the plate edge.
3. Determine the length of bearing.
thus,
8. Determine required plate thickness:
Note: Since the Mpl is expressed in units of kip-in./in., the plate thickness expressions can be formatted with-out the plate width (B) as such:
9. Use plate size:
N = 19 in.
B = 19 in.
t = 14 in.
B.5.2 Example: Large Moment Base Plate Design, Triangular Pressure Distribution Approach
Design the base plate shown in Figure B.4 for an ASD and LRFD required strength of 60 and 90 kips, respectively, and moments from the dead and live loads equal to 480 and 720 kip-in., respectively. The ratio of the concrete to base plate area (A2/A1) is 4.0. Bending is about the strong axis for the wide flange column W8×31 with d = bf = 8 in.; Fy of the base plate and anchor rods is 36 ksi and fc′ of the concrete is 3 ksi.
1.
LRFD ASD
tM
Fu requ crit
y
kip-in.
ksi in.
=
=××
=
4
4 11 1
0 90 361 17
φ
.
..
tM
Fa reqa crit
y
kip-in.
ksi in.
=
=× ×
=
4
4 7 68 1 67
361 19
Ω
. .
.
LRFD ASD
P
M
P
A
u
u
p
=
=
=
≤
90
720
0 60 0 85 3 0 2
0 60 1 71
kips
kip-in.
φ. ( . )( . )( )
. ( . )(( . )3 0
P
M
P
A
a
a
p
=
=
=
≤
60
480
0 85 3 0 2
2 50
1 7 3 01
kips
kip-in.
Ω( . )( . )( )
.
( . )( . ))
.
.
2 50
2 041
P
Ap
Ω= ksi
LRFD ASD
e = 720 kip-in./90 kips = 8.00 in. e = 480 kip-in./60 kips = 8.00 in.
Figure B.4. Design example with large eccentricity.
LRFD ASD
′ =× ×
=
f3 06 14 12 5
2268
. . ksi in. in.
kips
′ =× ×
=
f 2 04 14 12 5
2178
. . ksi in. in.
kips
LRFD ASD
A=
−−
×
× ×( )+
×
268268 4
3 06 146
90 5 5 720
3 06 143
2 .
.
.
= in.5 27.
A=
−−
×
× ×( )+
×
178178 4
2 04 146
60 5 5 480
2 04 143
2 .
.
.
= in.5 27.
φP
Ap
1
3 06= . ksi
AISC Design Guide 1, 2nd EditionBase Plate and Anchor Rod Design
Verification Example
DESIGN GUIDE 1, 2ND EDITION / BASE PLATE AND ANCHOR ROD DESIGN / 61
Anchor rods are placed at a 12-in. edge distance. The required moment strength, Mu pl or Ma pl, for a 1-in. strip of plate due to the tension in the anchor rods is
The required moment strength due to the bearing stress distribution is critical.
The required plate thickness is:
Use a 14 × 14 × 1-in. base plate.
4. Determine the required tensile strength of the anchor rod.
5. Determine the required plate thickness.
The moment for this determination is to be taken at the critical plate width. This is determined by assuming that the load spreads at 45° to a location 0.95d of the col-umn. The width is then taken as twice the distance from the bolt to the critical section for each bolt, provided that the critical section does not intersect the edge of the plate.
The critical section, as shown in Figure B.5, is at 14 − 0.95(8)/2 = 3.2 in.
The required moment strength, Mu pl or Ma pl, for a 1-in. strip of plate, determined from the bearing stress distri-bution in Figure B.4, is
LRFD ASD
T
T T
u
rod u
=× ×
−
== =
3.06 ksi 5.27 in. 14 in. kips
kips2
90
22 8
2 11
.
/ ..4 kips
T
T T
a
rod a
=× ×
−
== =
2.04 ksi 5.27 in. 14 in. kips
kips2
60
15 2
2 7
.
/ .660 kips
LRFD ASD
Mu pl =×( )
+−
1 20 3 2
2
3 06 1 20
2
23
. .
( . . )
ksi in.
ksi ksi ××( . )3 2
2
2 in.
= 12.5 in-kips/in.
Ma pl
ksi in.
ksi ksi
=×( )
+−
0 80 3 2
2
2 04 0 80
2
23
. .
( . . )) ( . )× 3 2
2
2 in.
= 8.33 in-kips/in.
LRFD ASD
M u pl =−
−
kips in. in.
in in.
22 8 3 2 1 5
2 3 2 1 5
. ( . . )
( . . . )
in.-kips/in.=11 4.
M a pl =−
−=
kips in. in.
in. in.
i
15 2 3 2 1 5
2 3 2 1 5
7 60
. ( . . )
( . . )
. nn.-kips/in.
LRFD ASD
t p = ×=
4 12 5
0 90 361 24
( . )
..
in.-kips
ksi in. t p = =
4 8 33 1 67
361 24
( . )( . ).
in.-kips
ksi
Figure B.5. Critical plate width for anchor bolt (tension side).
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Verification Example
Javier Encinas, PE
Base Plate Verification
Page # ___
7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
GEOMETRY
Column Section .................
Width Length
Column ..........
Plate ..............
ConcreteSupport
Rod Offset .....
Thickness of Grout ............
Wp1
Wp2
Lp1
Lp2
W8X31
8.0 8.0
14.0 14.0
14.0 14.0
14.0 14.0
5.5 5.5
1.5
in
in
in
in
in
in
OK
OK
OK
OK
SERVICE LOADS (ASD)
Vertical Load P ................
Bending Moment M .........
Horizontal Load V ............
Design Eccentricity e .......
Design Eccentricity Is > L/2
60.0
40.0
0.0
8.0
kip
k-ft
kip
in
MATERIALS
Plate Steel Strength Fy ....
Pier Concrete Strength f'c
36.0
3.0
ksi
ksi
AXIALLY LOADED PLATES
Cantilever Model
Bearing Stress fp .............
Critical Section @ Long m
Critical Section @ Short n
Plate Thickness tp ..........
0.31
3.20
3.80
0.64
ksi
in
in
in
OK
Thornton Model
Bearing Strength Fp/Ω .....
Critical Section @ Int λn' .
Design Moment @ Plate ...
Plate Thickness tp ............
2.04
0.81
0.10
0.14
ksi
in
k-in/in
in
BASE PLATES WITH MOMENT
Blodgett Method
Max. Bearing Stress fp ......
Bearing @ Critical Section
Moment @ Critical Section
Moment due to Rod Tension
Design Moment @ Plate ....
Plate Thickness tp .............
1.64
0.88
7.11
4.86
7.11
1.15
ksi
ksi
k-in/in
k-in/in
k-in/in
in
OK
DeWolf Method
Max. Bearing Stress fp ......
Bearing @ Critical Section
Moment @ Critical Section
Moment due to Rod Tension
Design Moment @ Plate ....
Plate Thickness tp .............
2.04
0.80
8.34
3.86
8.34
1.24
ksi
ksi
k-in/in
k-in/in
k-in/in
in
OK
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Verification Example
Javier Encinas, PE
Base Plate Verification
Page # ___
7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
ANCHORAGE DESIGN
Rod Material Specification .........
Anchor Rod Size ..
F1554-36
(4) Rods , fya = 36.0 ksi, futa = 58.0 ksi
1" diam. x 16.0 in emb.
Concrete Is Cracked at Service Load Level
Tension Analysis (kip)
Total Tension Force N ..........
Tension Force per Rod Ni ....
Anchor Reinf: Use 2 Bars #5 per Rod
15.4
7.7
kip
kip
Failure Mode Ω Nn N / Nn/Ω
Steel Strength Nsa
Rebars Strength Nrg
Conc. Breakout Ncbg
Pullout Strength Npn
Side Blowout Nsbg
N / Nn/Ω Tension Design Ratio .... OK
2.00
2.00
2.00
2.00
2.00
35.1
74.4
N.A.
36.0
N.A.
0.44
0.41
N.A.
0.43
N.A.
0.44
Shear Analysis (kip)
Shear Taken by Anchor Rods only
Total Shear Force V ........... 0.0 kip
Shear Force per Rod Vi ...... 0.0 kip
All Anchor Rods Are Effective
No Reinforcing Bars Provided
Failure Mode Ω Vn V / Vn/Ω
Steel Strength Vsa
Rebars Strength Vrg
Conc. Breakout Vcbg
Conc. Pryout Vcpg
2.31
2.31
2.14
2.14
16.9
N.A.
11.9
52.8
0.00
N.A.
0.00
0.00
0.00V / Vn/Ω Shear Design Ratio ...... OK
Tension-Shear Interaction
Combined Stress Ratio ........... 0.25 OK
SUMMARY OF RESULTS
Design Moment @ Plate ...
Plate Thickness tp ............
Max. Bearing Stress fp .....
Bearing Strength Fp/Ω ......
fp / Fp/Ω Design Ratio ..............
8.3
1.24
2.04
2.04
1.00
k-in/in
in
ksi
ksi
OK
DESIGN IS DUCTILE
DESIGN CODES
Steel design .............
Base plate design ....
Anchorage design ...
AISC 360-10 (14th Ed.)
AISC Design Series # 1
ACI 318-11 Appendix D
2
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Javier Encinas, PE
Base Plate Verification
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ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
Tension Breakout Shear Breakout
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Verification Example
Javier Encinas, PE
Base Plate Verification
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7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
Column Section .................
Width Length
Column ..........
Plate ..............
Concrete
Support
Rod Offset .....
Thickness of Grout ............
Wp1
Wp2
Lp1
Lp2
in
in
in
in
in
in
OK
OK
OK
OK
Vertical Load P ................
Bending Moment M .........
Horizontal Load V ............
Design Eccentricity e .......
Design Eccentricity Is > L/2
8.0
kip
k-ft
kip
in
Plate Steel Strength Fy ....
Pier Concrete Strength f'c
ksi
ksi
Bearing stress 60.0 / (14.0 * 14.0) = 0.3 ksi
Bearing strength = 0.85 * 3.0 * = 5.1 ksi ACI 10.14.1
Under-strength factor Ω = 2.50 ACI 9.3.2.4
Bearing strength ratio = =0.3
2.0 / 2.50= 0.15 < 1.0 OK
Critical section m =
Critical section n =
0.5 * (14.0 - 0.95 *8.0) = 3.2 in
0.5 * (14.0 - 0.80 *8.0) = 3.8 in
AISC-DG#1 3.1.2
[4 * 8.0 * 8.0
(8.0 + 8.0)²] * 0.15 = 0.15 AISC-DG#1 3.1.2
=+ -
= 0.40
= = 2.0 in
Controlling section Max (3.2, 3.8, 0.40 * 2.0) = 3.8 in
Plate moment 0.3 * 3.8² / 2 = 2.2 k-in/in
Plate thickness = 3.8 * = 0.64 in AISC-DG#1 3.1.2
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Verification Example
Javier Encinas, PE
Base Plate Verification
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7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
Eccentricity 40.0 * 12 / 60.0 = 8.0 in > L / 6 = 14.0 / 6 = 2.3in
Bearing length
Y = 1.5 * (14.0 / 2 + 5.5) - 0.5 * [ + ] - = 5.3 in AISC-DG#1 B.4.2
Max bearing stress 2.0 ksi
Tension 2.0 * 5.3 * 14.0 / 2 - 60.0 = 15.4 kip AISC-DG#1 B.4.2
Bearing at critical section 2.0 * (1 - 3.2 / 5.3) = 0.8 ksi
Moment due to bearing
Mb = 0.8 * 3.2² / 2 + (2.0 - 0.8) * 3.2² / 3 = 8.3 k-in/in
Moment due to tension
Mt = 7.7 * [3.2 - (14.0 / 2 - 5.5)] / [2 * (3.2 - (14.0 / 2 - 5.5))] = 3.9 k-in/in
Plate thickness = = 1.24 in
AISC-DG#1 3.1.2
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Verification Example
Javier Encinas, PE
Base Plate Verification
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7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
Rod Material Specification ...... F1554-36 , Use (4) Rods , fya = 36.0 ksi, futa = 58.0 ksi
Anchor Rod Size .... 1" diam. x 16.0 in emb. , Ase = 0.61 in² , Abrg = 1.50 in²
ACI D.5
Total tension force N = 15.4 kip , # of tension rods = 2 , Tension force per rod Ni = 7.7 kip
- Steel strength of anchors in tension ACI D.5.1
Steel strength 0.606 * 58.0 = 35.1 kip ACI Eq. (D-2)
Under-strength factor Ω = 2.00 ACI D.4.3
Steel strength ratio = =7.7
35.1 / 2.00= 0.44 ACI D.4.1.1< 1.0 OK
- Concrete breakout strength of anchors in tension ACI D.5.2
Anchor reinforcement: Use 2 bars #5 per rod
Bar strength 0.31 * 2 * 2 * 60 = 74.4 kip
Under-strength factor Ω = 2.00 ACI D.5.2.9
Bar strength ratio = =15.4
74.4 / 2.00= 0.41 ACI D.4.1.1< 1.0 OK
Effective embedment 19.50 / 1.5 = 13.00 in ACI D.5.2.3
Anchor group area
Anc = (19.5 + 8.5) * (8.5 + 11.0 + 8.5) = 784.0 in² ACI D.5.2.1
Single anchor area 9 * (13.0)² = 1521.0 in² Eq. (D-5)
Single anchor strength = 24 = 61.6 kip Eq. (D-6)
Eccentricity factor 1.00 (No eccentric load) ACI D.5.2.4
Edge effects factor = 0.7 + 0.38.5
1.5 * 13.0= 0.83 ACI D.5.2.5
Cracking factor 1.00 (Cracked concrete at service load level) ACI D.5.2.6
Breakout strength
784.0
1521.01.00 * 0.83 * 1.00 * 61.6 = 26.4 kip Eq. (D-4)
Under-strength factor Ω = 2.00 ACI D.4.3
Breakout strength ratio = =15.4
26.4 / 2.00= 1.17 ACI D.4.1.1> 1.0 NG
Bar strength ratio controls (0.41 < 1.17) ACI D.5.2.9
- Concrete pullout strength of anchors in tension ACI D.5.3
Single anchor strength 8 * 1.50 * 3.0 = 36.0 kip ACI Eq. (D-14)
Cracking factor 1.00 (Cracked concrete at service load level) ACI D.5.3.6
Pullout strength 1.00 * 36.0 = 36.0 kip ACI Eq. (D-13)
Under-strength factor Ω = 2.00 ACI D.4.3
Pullout strength ratio = =7.7
36.0 / 2.00= 0.43 ACI D.4.1.1< 1.0 OK
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Verification Example
Javier Encinas, PE
Base Plate Verification
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7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
- Concrete side-face blowout strength of anchors in tension ACI D.5.4
Side-face blowout Nsbg = N.A. (Embed < 2.5 Ca₁ , 16.0 < 2.5 * 8.5 = 21.3) ACI D.5.4.1
Tension Design Ratio = = 0.44 < 1.0 OK ACI D.4.1.1
ACI D.5
Shear resisted by Anchor Rods only
Total shear force V = 0.0 kip , Shear per rod Vi = 0.0 kip ,
(anchor rods are welded to the base plate)
(all anchor rods are effective)
- Steel strength of anchor rods in shear
Steel strength 0.6 * 0.61 * 58.0 * 0.80 = 16.9 kip ACI D.6.1.2
Under-strength factor Ω = 2.31 ACI D.4.3
Steel strength ratio = =0.0
16.9 / 2.31= 0.00 < 1.0 OK ACI D.4.1.1
- Concrete breakout strength of anchors in shear ACI D.5.2
No Reinforcing bars provided
Anchor group area
Avc = (1.5 * 8.00) * (8.50 + 11.00 + 8.50) = 336.0 in² ACI D.6.2.1
Single anchor area 4.5 * (8.00)² = 288.0 in² Eq. (D-32)
Single anchor strength
Vb = Vb = 11.2 kip Eq. (D-33)
Eccentricity factor 1.00 (No eccentric load) ACI D.6.2.5
Edge effects factor = 0.7 + 0.38.50
1.5 * 8.0= 0.91 ACI D.6.2.6
Cracking factor 1.00 (Cracked concrete at service load level) ACI D.6.2.7
Thickness factor ACI D.6.2.8
Breakout strength
336.0
288.01.00 * 0.91 * 1.00 * 1.00 * 11.2 = 11.9 kip Eq. (D-31)
Under-strength factor Ω = 2.14 ACI D.4.3
Breakout strength ratio = =0.0
11.9 / 2.14= 0.00 < 1.0 OK ACI D.4.1.1
Breakout strength ratio controls (0.00 < 0.00) ACI D.6.2.9
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Verification Example
Javier Encinas, PE
Base Plate Verification
Page # ___
7/20/2014
ASDIP Steel 3.2.5 STEEL BASE PLATE DESIGN www.asdipsoft.com
- Concrete pryout strength of anchors in shear
Pryout strength 2.0 * 11.9 = 52.8 kip ACI D.6.3.1
Under-strength factor Ω = 2.14 ACI D.4.3
Pryout strength ratio = =0.0
52.8 / 2.14= 0.00 < 1.0 OK ACI D.4.1.1
Shear Design Ratio = = 0.00 < 1.0 OK ACI D.4.1.1
Combined Stress Ratio =
Combined Stress Ratio = + = 0.25 < 1.0 OK ACI RD.7
Anchorage design is ductile
Steel design ...................
Base plate design ..........
Anchorage design .........
AISC 360-10 (14th Ed.)
AISC Design Series # 1
ACI 318-11 Appendix D
5
